Carlos Beta
Carlos Beta is a non-octave equal temperament with step size about 63.833 cents[1], or almost exactly every fifth step of 94edo. It was invented by Wendy Carlos.
In this temperament, the interval of 11 steps approximates 3/2, that of 6 steps approximates 5/4, and that of 5 steps approximates 6/5.
Theory
Carlos optimized the tuning on 3/2, 5/4, and 6/5, such that the tuning divides the octave in [math]\displaystyle{ \frac{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)} }[/math] ≃ 18.799074 equal steps and the fifth in 10.996753 equal steps of 63.832933 cents each. It is thus very close to the equal division of the just perfect fifth into eleven parts of 63.8141 cents each (11ed3/2), corresponding to 18.8046edo.
Carlos Beta is related to the sycamore temperaments; betic and 5-limit sycamore in particular.
Lookalikes: 19edo, 11edf, 30edt, every 5th step of 94edo, every 4th step of 75edo
Intervals
| Degrees | Cents ~ Cents octave reduced | Approximate JI interval ~ octave reduced |
|---|---|---|
| 0 | 0 | |
| 1 | 64 | |
| 2 | 128 | |
| 3 | 191 | |
| 4 | 255 | |
| 5 | 319 | 6/5 |
| 6 | 383 | 5/4 |
| 7 | 447 | |
| 8 | 510.5 | |
| 9 | 574 | |
| 10 | 638 | |
| 11 | 702 | 3/2 (exact) |
| 12 | 766 | |
| 13 | 830 | 13/8-ish |
| 14 | 893 | |
| 15 | 957 | |
| 16 | 1021 | |
| 17 | 1085 | 15/8 |
| 18 | 1149 | |
| 19 | 1211.5 ~ 11.5 | 2/1-ish |
| 20 | 1276 ~ 76 | |
| 21 | 1340 ~ 140 | |
| 22 | 1404 ~ 204 | 9/4~9/8 (exact) |
| 23 | 1468 ~ 268 | better 7/6 |
| 24 | 1532 ~ 332 | |
| 25 | 1595 ~ 395 | |
| 26 | 1659 ~ 459 | |
| 27 | 1723 ~ 523 | |
| 28 | 1787 ~ 587 | |
| 29 | 1851 ~ 651 | |
| 30 | 1914 ~ 714 | |
| 31 | 1978 ~ 778 | |
| 32 | 2042 ~ 842 | 13/4 ~ 13/8 (better) |
| 33 | 2106 ~ 906 | |
| 34 | 2170 ~ 970 | |
| 35 | 2233 ~ 1033 | |
| 36 | 2297 ~ 1097 |
Music
- See also: Category:Carlos Beta tracks
See also
Reference
- ↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43